Sunday, August 18, 2019

MA 330  Course Syllabus
History of Mathematics, an Introduction
Fall Semester 2019

1 Instructor
Prof. Richard Carey
Office: POT 965
E-Mail richard.carey@uky.edu
Phone: (859) 257-3745
Office Hours: MW 2-3 and by appt.

From The Bulletin of Course Descriptions:
A survey of the development of mathematics. Topics may include: the Egyptians and Babylonians,
mathematics of the Greek Classical Age, Euclid and the Alexandrian School,the Renaissance,
Fermat and the beginning of calculus, the work of Newton and Leibnitz, nineteenth
century geometry, analysis and set theory. Prequisite MA 114.
More specific research topics from your textbook and the web include:
From Geometry: Theory of area; famous construction problems; history of the parallel
postulate and non-euclidean geometry; Bolyai-Lobachevsky formula for the angle of parallelism
and distance:
                                                       tan α/2 = e^{−d/k}
where k is the constant whose square occurs in the proportionality factor for area to defect.

From Number Theory: The fundamental theorem of arithmetic; Fermat’s Christmas theorem;
Fermat’s Little theorem; Fermat’s Last theorem; Bernoulli formula for the sum of k-th
powers; prime number theorem, clock arithmetic and the Law of Quadratic-Reciprocity; p-adic
numbers; Diophantine equations, cryptology .

From Algebra: Complex numbers and the fundamental theorem of algebra, cubic and quartic
equations, solutions of equations of degree five or greater; algebra of quaternions; algebraic
number theory, algebra of matrices and vectors, axiomatic algebra - groups, rings and fields;
mathematics of the search engine.

From Calculus: Origins of calculus. Fundamenal Theorem of calculus as exemplified by
the theorems of Green, Stokes and Gauss; Maxwel’s electromagnetic equations, calculus of
variations and the principle of least action; infinite series which leads to celebrated formulas
such as
         e^{iπ} +1 = 0, and sum{ n=1 to infinity} 1(/n^2) =(π^2)/6.
.

From Probability: Statistical probability and gambling on Wall Street and casinos on the
boat or in Las Vegas and Macau, set theory and counting, The law of large numbers, the central
limit theorem.

2 Text:The text for the course is The History Of Mathematics, An Introduction; 7th edition.by
David M. Burton. This text is online at


 In addition there are multiple online references including the prominent
MacTutor History of mathematics archive. For fun check out the top 100 theorems list.


3 Grading Your course score will be the sum of two take-home exam assignments (100),
and a take-home final exam (130) The grading scale for the course will be as follows:
297-330 A; 264-296 B; 231-263 C; 198-230 D; < 198 E.
The Final Exam is due no later than 5 pm on Wednesday December 18.

4 Attendance: Grading for the course will be influenced by class attendance. You will be
allowed 4 unexcused absences, then for every missed class after that you will lose 10 points
from the possible 330. I will let you know later when roll begins.

5 Additional Course Policies: Course policy of academic accommodations due to disability:
If you have a documented disability that requires academic accommodations, please see
me as soon as possible during scheduled office hours. In order to receive accommodations
in this course, you must provide me with a Letter of Accommodation from the Disability
Resource Center Course policy for attendance: See the above. Make-up opportunities: The
instructor shall give the student an opportunity to make up the work and/or the exam missed
during an excused absence... implies the student shall not be penalized for the excused absence.
Verification of Absences: Students missing work due to an excused absence bear the
responsibility of informing the instructor about their excused absence within one week following
the period of the excused absence (except where prior notification is required) and
of making up the missed work. Course policy for submission of assignments: Students shall
return all assignments on the due date. No late assignments shall be accepted without an
excused absence. Course policy on academic integrity: All assignments, projects, and exercises
completed by students for this class should be the product of the personal efforts of the individual(
s) whose name(s) appear on the corresponding assignment. Misrepresenting others work
as ones own in the form of cheating or plagiarism is unethical and will lead to those penalties
outlined in the University Senate Rules (6.3.1 and 6.3.2) at the following website: http :
//www.uky.edu/USC/New/rulesregulations/index.htm. The Ombud site also has information
on plagiarism found at http : //www.uky.edu/Ombud.Course policy on classroom civility and
decorum: The university, college and department has a commitment to respect the dignity of
all and to value differences among members of our academic community. There exists the role
of discussion and debate in academic discovery and the right of all to respectfully disagree from
time to time. Students clearly have the right to take reasoned exception and to voice opinions
contrary to those offered by the instructor and/or other students (S.R. 6.1.2). Equally, a faculty
member has the right - and the respon- sibility - to ensure that all academic discourse occurs in
a context characterized by respect and civility. Obviously, the accepted level of civility would
not include attacks of a personal nature or statements denigrating another on the basis of race,
sex, religion, sexual orientation, age, national/regional origin or other such irrelevant factors.
Please note Senate Rule 6.4.7.A.1 has changed. The Registrar will retain a record of the Letter
of Warning for an academic offense. It will be available to third parties if the student authorizes
its release or the specific record is requested as part of a court-ordered subpoena. In the past,
the Registrar destroyed the record of the offense when the student graduated.

Wednesday, August 29, 2018

MA 322

MA 322
 Matrix Algebra, Fall 2018
Section 001
MWF 9:00 -9:50 CB 214

1 Instructor 
Richard Carey
Office: POT 965
E-Mail richard.carey@.uky.edu
Phone: (859) 257-3745
Office Hours: MW 2:30-3:30 and by appt.

TA 
Brian Davis 
E-Mail Brian.Davis@uky.edu
Math House

2 Course Goals
The course is an introduction to the study of simultaneous linear equations in several variables. For example, the description of the tangent space to an n-dimensional surface sitting in n + r  - dimensional Euclidean space is recognized as an n-dimensional vector subspace. A handy overview is presented in Linear Algebra-Wikipedia. 
 Recall that in Calculus 3 one started with the coordinatization of three dimensional space via Cartesian coordinates; then began the algebraization of geometry with the introduction of vectors - directed line segments. Geometric operations on line segments were interpreted as algebraic operations on vectors to give an algebra for vectors in both the plane and three  dimensional spaces. Not only does this include addition and multiplication by scalar quantities, it also provides two different types of multiplication - the dot and cross products. These products are geometrically defined and Calculus 3 spent some time applying vector algebra to the geometry of three dimensions. Now we begin a more unified theory which allows us to go to dimensions higher than 3.You shall see how  matrix algebra  is used to calculate with functions of more than one variable - a version of higher order arithmetic. For example, the derivative of a function from the plane to 3-space is properly regarded as a linear transformation which can be represented by a 3 by 2 matrix ( with 3 rows and 2 columns).Matrices can  be added, subtracted,  multiplied by scalars; compatible matrices may also be multiplied. 

3 Text
Linear Algebra and Its Applications, Fifth Edition | ISBN-13:  9780321982384  

Author(s): David C. Lay; Steven R. Lay; Judi J. Mcdonald

4 Grading
Your grade for the course will be based on two exams during the semester, a final exam,  and quizzes.  Each of the four components will count toward your grade. The term exams will count 100 pts each and the final 150 pts.  Quizzes count 100.   

5 Quizzes: (100 points)  There will be weekly  in- class quiz problems. I will give a selection of these problems prior to the time of the quiz.Your course score will be the sum of your test, and quiz scores.

 Attendance Policy:
Grading for the course will be influenced by class attendance.  You
will be allowed 4 unexcused absences; for every missed class after that you will lose 10 points on your final grade . 
Students are expected to attend each class meeting unless he or she has been excused by the instructor. Failure to attend class will result in a lower grade, and may result in failing the class. Absence due to illness or emergencies must be reported within a week. You may call the instructor’s office or email him at the numbers/address listed on the first page of this syllabus. When there is an excused absence, students will be given the opportunity to make up missed work and/or exams.

The following are typically accepted reasons for excused absences:

1. Serious illness.
2. Illness or death of a family member.
3. Approved University-related trips.
4. Major religious holidays.
5. Other circumstances found to be "reasonable cause for nonattendance.”

It is important to take each exam on schedule. Missed work may be made up only due to illness with  medical documentation or for other unusual (documented) circumstances. Students who have university excused absences or who have university-scheduled class conflicts with uniform examinations may arrange  with their instructor to take the exam at an alternate time. Work-related conflicts are neither university excused absences or university-scheduled absences. If you miss an exam, you receive a zero. You will be  eligible for a make-up only if you present a valid excuse to me before the exam. If you cannot find a reasonable arrangement for a make-up, contact the department DUS Alberto Corso. Students anticipating an absence for a major religious holiday are responsible for notifying the instructor in writing of anticipated absences due to their observance of such holidays no later than the last day for adding a class. Information regarding dates of major religious holidays may be obtained through the the religious liaison.



Monday, August 20, 2018




Ma 214 Fall 2018

Syllabus  
Fall Semester 2018
MA 214 CalculusIV 
Section 004
 MWF 1:00 – 1:50
 CB 214


1 Instructors

Prof. Richard Carey 
Office: POT 965
E-Mail richard.carey@uky.edu
Phone: (859) 257-3745
Office Hours: MW 2:30-3:30pm  & by appt.

TA
Nandita Sahajpal
E-Mail nandita.sahajpal@uky.edu

office hour on Wednesday from 3:00-4:00 PM in the Klein room in Mathskeller (CB 063). 
Students can also contact me via email to make an appointment to meet me at my office. 
My office is in the Math House (654 Maxwelton Ct, Lexington, KY 40508-3225, USA).
The email that the students can use for direct questions about Webwork or make appointments is nandita.sahajpal@uky.edu. The students can expect to receive replies to the emails they send between 4:00 PM-6:00 PM on weekdays.
Moreover Joel Klipfel( Grader for Ma 214, Sec 1&2) has his office hour from 2-3:00 PM on Wednesday every week in the Klein Room; students may go to his office hours as well if they need help).

2  Text

The text for the course is 

Differential Equations with Applications and Historical Notes, Third Edition, by George F. Simmons

3  Material 

Chapters 1 through 5, 9.  Some material will be omitted..

"This is a course in ordinary differential equations. Emphasis is on first and second order equations and applications. The course includes series solutions of second order equations and Laplace transforms."From the University of Kentucky bulletin. 

4 Grading
The  course grade  will be computed (with 90-100% is an 80-89% is B 70-79%  is C,
60-69%  D, 50-59% is E) on the basis of 500 points earned as follows:


                                     in-class exams {October, November}      100  points each
                              Final Exam                                                   150  points 

 webwork link:
   
https://webwork.as.uky.edu/webwork2/MA214004F18/


5  Attendance 
Grading for the course will be influenced by class attendance. You will be allowed 4 unexcused absences, then for every missed class after that you will lose 10 points from the possible 450. I will let you know when roll begins.


6  Makeups

Individuals who miss a quiz or an exam will be given a zero unless they have an official excuse. Makeup quizzes or exams will be permitted only for excused absences makeups will be given during \dead week", that is, the last week of classes. 


Faculty Senate Rule 5.2.4.2 guideline for excused absnce:

(a) serious illness, (b)  or death of family member, (c) University-related trips,d) major religious holidays, and (e) other circumstances found to t \reasonable cause for nonattendance" by the professor. As required by University rules, you must present full documentation in order to request makeup work for a valid absence. Senate rule 5.2.4.2 states that faculty have the right to request appropriate verification when students claim an excused absence because of illness or death in the family. Appropriate notification of absences due to University-related trips or a major religious holiday is required no later than 7 days prior to the absence.

7  Cheating 


Don't do it. It is an extremely serious offense. As a minimum response, I will give a zero to the offender. 

8  Plagiarism 

Plagiarism includes copying from outside sources, including internet sources. If charged, at minimum you will receive a zero. Maximum penalties include being suspended, dismissed or expelled from the University. For further information, consult the Faculty Senate rules.




  
.

Friday, August 19, 2016

MA 341 Topics in Geometry 
 Course Syllabus  
Fall Semester 2017

Section 001
 MWF 11:00 – 11:50
 CB 341


1 Instructors
Prof. Richard Carey

Office: POT 965

E-Mail richard.carey@uky.edu

Phone: (859) 257-3745

Office Hours: MW 3:15-4:15 and by appt.


2  Text: The text for the course is 

Euclidean and Non-Euclidean Geometries; Development and History. 4th edition

Taken from Math Reviews:
The book gives an account of the discovery of non-Euclidean geometry and the subsequent rebuilding of the foundations of Euclidean geometry. It is written for three kinds of readers prospective high-school teachers (presented with a rigorous treatment of the foundations of Euclidean geometry and an introduction to hyperbolic and elliptic geometries, liberal arts students (introduced to the history and philosophical aspects of the subject), mathematics majors (who are given challenging exercises and a historical perspective).
The author uses modified versions of Hilbert's axioms. Following Tarski, he replaces the general (Dedekind's) axiom of continuity by two \elementary" specializations of it. Dedekind's axiom itself is used only in the treatment of hyperbolic geometry (to prove the existence of limiting parallel rays). A specific feature is that new results are developed in the exercises and then used in subsequent chapters. This ensures the reader's activity and his genuine understanding. Some exercises consist of philosophical
or historical essay topics. A few reasonable innovations in terminology are implanted or newly introduced: \neutral geometry" (to replace the traditional term \absolute
geometry"), \asymptotic" and \divergent" for two kinds of parallels in hyperbolic geometry. A well classified bibliography (74 items), as well as a collection of expressive portraits (Legendre, Hilbert, Lambert, Gauss, Lobacevski, Beltrami, Klein, Poincare, Einstein, Godel, Riemann), enrich the contents of the book.


3  Material Chapters 1 through 6, some material will be omitted. We will also study portions of 7 and 8.
   
4  Grading: The course grade will be computed (with 90-100% A, 80-89% B, 70-79% C,60- 69% D, 0-59% E) on the basis of 435 points earned as follows:

                            2 take-home exams     100 points each
                            quiz / homework           100 points


                               take- home final            135 points
  
Exams will be allowed approximately nine days to submit.

 Exam 1 around October 7, Exam 2 around Nov 7.
 

5 Attendance: Grading for the course will be influenced by class attendance. You will be allowed 4 unexcused absences, then for every missed class after that you will lose 10 points from the possible 435. I will let you know when roll begins.



6  Makeups: Individuals who miss a quiz or an exam will be given a zero unless they have an official excuse. Makeup quizzes or exams will be permitted only for excused absences makeups will be given during \dead week", that is, the last week of classes.

Faculty Senate Rule 5.2.4.2 defines acceptable reasons for excused absences to be:

(a) serious illness, (b)  or death of family member, (c) University-related trips,d) major religious holidays, and (e) other circumstances found as reasonable cause for nonattendance" by the professor. As required by University rules, you must present full documentation in order to request makeup work for a valid absence. Senate rule 5.2.4.2 states that faculty have the right to request appropriate verification when students claim an excused absence because of illness or death in the family. Appropriate notification of absences due to University-related trips or a major religious holiday is required no later than 7 days prior to the absence.

Cheating:
Don't do it. It is an extremely serious offense. As a minimum response, I will give a zero to the offender.
 
Plagiarism Plagiarism includes copying from outside sources, including internet sources. If charged, at minimum you will receive a zero. Maximum penalties include being suspended, dismissed or expelled from the University. For further information, consult the Faculty Senate rules.

9 Reserve: The instructor reserves the right to modify this syllabus at any time.

 
10   UK Senate Policies

Student Learning Outcomes (Arts & Sci.; Creativity Requirement):

Here’s what you will be able to do upon completing this class:

1. Define and distinguish among different approaches to geometry.
2. Demonstrate the application of logic, laws, and constraints
3. Demonstrate the ability to critically analyze work produced by other students.
4. Recognize the essential importance and significance of posing your own questions/problems.

Mid-term Grades

Mid-term grades will be posted in myUK by the deadline established in the Academic Calendar (http://www.uky.edu/registrar/content/academic-calendar)

Excused Absences (boilerplate):

Students need to notify the professor of absences prior to class when possible. S.R.
5.2.4.2 defines the following as acceptable reasons for excused absences: (a) serious illness, (b) illness or death of family member, (c) University-related trips, (d) major religious holidays, and (e) other circumstances found to fit “reasonable cause for nonattendance” by the professor.

Students anticipating an absence for a major religious holiday are responsible for notifying the instructor in writing of anticipated absences due to their observance of such holidays no later than the last day in the semester to add a class. Information regarding dates of major religious holidays may be obtained through the religious liaison, Mr. Jake Karnes (859-257-2754).

Students are expected to withdraw from the class if more than 20% of the classes scheduled for the semester are missed (excused or unexcused) per university policy.

Verification of Absences (boilerplate)

Students may be asked to verify their absences in order for them to be considered excused. Senate Rule 5.2.4.2 states that faculty have the right to request “appropriate verification” when students claim an excused absence because of illness or death in the family. Appropriate notification of absences due to university-related trips is required prior to the absence.

Academic Integrity (boilerplate):

Per university policy, students shall not plagiarize, cheat, or falsify or misuse academic
records. Students are expected to adhere to University policy on cheating





Thursday, August 18, 2016

MA 432G Course Syllabus  
Fall Semester 2016

Section 001
 MWF 01:00 – 01:50
 CB 345


1 Instructors
Prof. Richard Carey

Office: POT 965

E-Mail richard.carey@uky.edu

Phone: (859) 257-3745

Office Hours: MW 3-4:30pm  & by appt.


2  Text: The text for the course is 

Differential Equations with Applications and Historical Notes, by George F. Simmons, 2n edition. Here is a review of the book:

Format: Hardcover
I've taught upper division students from this book (and the first edition) 5-6 times for over a decade. I remain impressed by the broad range of topics from which the teacher and reader can select. As with his excellent calculus textbook, the author tries to show students how mathematics is a human activity, a subject that developed in response to actual needs and which is still lively and developing. No part of mathematics illustrates this development better than the topic of differential equations, which was invented to solve pressing problems in astronomy. One example: In Newton's time, accurate location of position on the open seas was an unsolved problem, crucial to commerce. New techniques from differential equations led to the ready calculation of tables which, together with the invention of Harrison's sea-going chronometer, effectively solved the navigation problem. Differential equations lie at the core of the physical sciences and engineering and are proving increasingly valuable in biology and medicine. Simmons' book will not appeal to readers who want merely recipes with examples of their use. Such readers might prefer the excellent books from the Schaum's Outline Series. Those readers who want to see vital mathematics well presented, those readers who think that mathematics stops at trigonometry or the calculus, those readers who want to use differential equations intelligently, and those readers who just like a cracking good mathematics story should get a copy of Simmons' book and read.
Nathaniel Grossman Professor of Mathematics, UCLA

 3  Material Chapters 3 through 9. Some material will be omitted.

4  Grading: The course grade will be computed (with 90-100% A, 80-89% B, 70-79% C,60- 69% D, 0-59% E) on the basis of 435 points earned as follows:

                                     2 take-home exams           100 points each
                                     homework assignments     100 points


                                     Final exam                           135 points
 Exams will be allowed approximately nine days to submit.
 Exam 1 around October 7, Exam 2 around Nov 7.
 

4  Attendance: Grading for the course will be influenced by class attendance. You will be allowed 4 unexcused absences, then for every missed class after that you will lose 10 points from the possible 435. I will let you know when roll begins.



 5  Makeups: Individuals who miss a quiz or an exam will be given a zero unless they have an official excuse. Makeup quizzes or exams will be permitted only for excused absences makeups will be given during \dead week", that is, the last week of classes.

Faculty Senate Rule 5.2.4.2 defines acceptable reasons for excused absences to be:

(a) serious illness, (b)  or death of family member, (c) University-related trips,d) major religious holidays, and (e) other circumstances found to t \reasonable cause for nonattendance" by the professor. As required by University rules, you must present full documentation in order to request makeup work for a valid absence. Senate rule 5.2.4.2 states that faculty have the right to request appropriate verification when students claim an excused absence because of illness or death in the family. Appropriate notification of absences due to University-related trips or a major religious holiday is required no later than 7 days prior to the absence.

Cheating
Don't do it. It is an extremely serious offense. As a minimum response, I will give a zero to the offender.
 
7 Plagiarism Plagiarism includes copying from outside sources, including internet sources. If charged, at minimum you will receive a zero. Maximum penalties include being suspended, dismissed or expelled from the University. For further information, consult the Faculty Senate rules.

8 Reserve: The instructor reserves the right to modify this syllabus at any time.